# How bad would tides be on an habitable moon orbiting a gas giant in a 5:2 resonance (meaning not actual tidal locking)?

I have been working on an habitable moon (roughly 0.7 to 0.9 times the mass of the earth) orbiting a gas giant about 3 times the mass of jupiter and I have been thinking about a scenario in which I'd place it at an orbit further away from the gas giant but in a 5:2 spin-orbit resonance thus ensuring that it would still have an earth-like day night cycle.

However, I have been adamant on making that scenario canon because the moon would effectively rotate within the tidal bulges that would form due to the gas giant's gravitational pull and I figured that it would make tides really really bad for the continents. Still I never let go completely of the idea and now I'd like to have some certitude on the matter.

Here is a bit more data:

Mass of the moon=0.7-0.9 earths

Structure of the moon: Molten iron core, metal rich mantle (5-10% compared with earth's 5%), oceans covering about 60 to 65% of the surface

Mass of the gas giant=3 Jupiters about 951 Earths

Distance between the moon and the gas giant: 1002900 kms

Rotation: 36 hours

Orbital period: 90 hours

Resonance: 5:2

Eccentricity=0.025

How bad would tides be on my world? And in case they were apocalyptic...how can I can mitigate them?

I have bad news. First consider earth. The tidal forces of the moon on the earths surface are 20 times weaker than the tidal forces of the earth on the moon's surface.

We can calculate the tidal force using the equation: Because wolfram alpha is amazing, we can just type it all in. I estimated 0.8 earth radius for the radius of the moon. We get a final result of 0.00384 m/s^2. While this seems like a small number -- do not be fooled. This is 3500 times larger than the value for the moon's effect on the earth.

When I reached this point I did some other math. Assuming an circular orbit, the central planet would need to have a density of 1.3453 kg/m^3 to maintain a 90-hour orbital period. Given the mass of 3 jupiters, this means the planet's volume is 4*10^27 m^3. Assuming it's a sphere, the planet's radius would then be 10^9 roughly, which is 1000 times greater than your orbital distance.

To sum up, tidal forces would be strong enough to destroy the planet, but it would be moot because the moon would be well inside the planet it orbited. I'm afraid you'll need to tweak some of the planet's parameters.

• Great answer @Carson. Would you mind explaining why the orbital period implies such a low density though? Aug 18, 2021 at 20:09
• Flows will workout some channels like river networks flowing east west or something, can be quite interesting landscape and effects on continental stuff. Problems with fresh water can be anticipated, hm quite interesting situation. To note, average density of Jupiter is 1326 kg/m3, same for the sun is 1410 kg/m3, so it safe to say a diameter of that planet is about 200'000 km. Roche limit is 78000km, and if you talk about orbital period associated with it it meaningless in the situation. However good attempt, highlighting interesting aspects of the system Aug 18, 2021 at 21:08
• Carson. Your calculations for the size of my gas giant are completely off, while it would be 3 times as massive as jupiter the size would be largely the same, I looked it up, the size of gas giants caps at the size of jupiter. Plus there is no way that the tidal forces could rip the planet apart, since it would be far beyond the roche limit. But I do reckon with the assessment about the strenght of the tides... how bad is that translated in ocean tides? Aug 18, 2021 at 22:11
• @JuimyTheHyena - This answer gives an equation for determining the relative heights of tides. 3,500 times seems like you'd end up with Interstellar-level waves. Sep 6, 2021 at 4:12
• IronEagle It also says that the real kicker is the form of the ocean, on my world areas that are contignous open oceans aren't really that present there are many island chains and the deep basins are relatively small. What do you think about that? Sep 6, 2021 at 7:42